ANALYSIS OF THE MULTIGRID FMV CYCLE ON LARGE-SCALE PARALLEL MACHINES

On serial computers it is well known that the multigrid FMV cycle is p referable to the V cycle both asymptotically and in practical use over a wide range of applications. However, on massively parallel machines , the parallel efficiency of the FMV (full multigrid V cycle) scheme i s noticeably lower than that of the V cycle due to a large percentage of time spent on coarse grids. Thus the question arises: are the addit ional coarse grid computations within the FMV cycle warranted on massi vely parallel machines? To answer this, a number of issues are address ed regarding parallel FMV cycles: what efficiencies can be achieved; h ow do these compare with V cycle efficiencies; are FMV cycles still pr eferable to V cycles in a massively parallel environment? A model is u sed to analyze the efficiency of both FMV and V cycles as a function o f relaxation efficiency. Using this model, the standard FMV grid-switc hing criterion is modified to incorporate the efficiency of the coarse grid processing. Numerical results obtained from a multigrid implemen tation on a 1024-processor nCUBE 2 are used in conjunction with the mo del to quantify the performance and efficiency of the FMV cycle. Final ly, comments are made regarding limitations of parallel processors bas ed on FMV efficiencies.